(11b^2+7b-12)-(15b^2-19b-21)=0

Solution for (11b^2+7b-12)-(15b^2-19b-21)=0 equation:

(11b^2+7b-12)-(15b^2-19b-21)=0

We get rid of parentheses

11b^2-15b^2+7b+19b-12+21=0

We add all the numbers together, and all the variables

-4b^2+26b+9=0

a = -4; b = 26; c = +9;
Δ = b2-4ac
Δ = 262-4·(-4)·9
Δ = 820
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{205}}{2*-4}=\frac{-26-2\sqrt{205}}{-8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{205}}{2*-4}=\frac{-26+2\sqrt{205}}{-8}
$